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PREPRINT. Computational Geometry: Theory and Applications,8(3):115122,5516 On the Difficulty of Range Searching

Summary: PREPRINT. Computational Geometry: Theory and
Applications,8(3):115­122,5516 On the Difficulty of Range Searching
Arne Andersson \Lambda Kurt Swanson \Lambda
Dept. of Computer Science, Lund University,
Box 118, S­221 00 LUND, Sweden
We consider the general problem of (2­dimensional) range reporting
allowing arbitrarily convex queries. We show that using a traditional
approach, even when incorporating techniques like those used in fusion
trees, a polylogarithmic query time can not be achieved unless more
than linear space is used. Our arguments are based on a new non­
trivial lower bound in a model of computation which, in contrast to
the pointer machine model, allows for the use of arrays and bit ma­
nipulation. The crucial property of our model, Layered Partitions, is
that it can be used to describe all known algorithms for processing
range queries, as well as many other data structures used to represent
multi­dimensional data. We show
log n


Source: Andersson, Arne - Department of Information Technology, Uppsala Universitet


Collections: Computer Technologies and Information Sciences